Positive streamer in a weak field in air: A moving avalanche-to-streamer transition

Two-dimensional (2D) simulation of a positive streamer in air between a point anode and a plane cathode is performed within the scope of a diffusion-drift model. A fine structure of streamer head is obtained. Based on the simulation results, the head is treated as a moving region of an avalanche-to-streamer transition (AST). Using ``empirical'' relations, which follow from 2D simulations, and applying the Meek's concept of an AST, two simple analytical models of streamer dynamics in a weak field are offered. The isolated head model gives results which correspond well to that of 2D simulations. The potential model qualitatively explains an effect recently detected in experiment of streamer expansion in a weak external field. Both models allow one to calculate the streamer velocity, number density of electrons, and radius of the plasma channel from a single input parameter.